Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
242 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q16×#10596831 | C2 | semidirect |
| 4. #22608004 | C2 | semidirect |
| 6. C16×#10596831 | C2 | semidirect |
| 7. C73×#1332 | C2 | semidirect |
| 26. #14556534 | C8 | semidirect |
| 56. #11924003 | C2×C8 | semidirect |
| 59. Q16×C73 | C2×C8 | semidirect |
| 88. #10596831 | SD32 | semidirect |
| 110. #1332 | D73 | semidirect |
| 113. C73 | C8×SD32 | semidirect |
| 154. Q16 | C8×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556534 | 2 |
| Q16×#10596831 | 2 |
| #22608725 | 2 |
| #22608004 | 2 |
| #22607893 | 2 |
| C16×#10596831 | 2 |
| C73×#1332 | 2 |
| C8×SD32 | 73 |